The present invention relates to methods and apparatuses for determining the reserve quality of an oil well delivering a given fluid coming from a productive layer, by measuring the response R of the well.
Oil is produced from wells made in oil fields, and such oil fields are to be found in various different types of ground and subsoil which do not all have the same production quality. This quality is represented essentially by the productivity index IP of the well which depends on the radius of the well rw, the drainage radius Re of the well, the viscosity xcexc of the recoverable oil, and also the transmissivity of the productive layer which is defined as the product of its permeability k multiplied by its height h, and possibly also on any clogging of the pores in the rock in the vicinity of the wall of the well which is quantified by a dimensionless parameter S commonly referred to by the person skilled in the art under the generic term xe2x80x9cskinxe2x80x9d. This productivity index is given by the following formula:   IP  =            2      ⁢              xe2x80x83            ⁢      π      ⁢              xe2x80x83            ⁢      k      ⁢              xe2x80x83            ⁢      h              μ      [                        ln          ⁡                      (                                          R                e                                            r                w                                      )                          -        0.75        +        S            ]      
where ln represents the natural logarithm.
The productivity index IP is a direct measure of the ease with which oil can flow into the well under the effect of a drop xcex94P in the mean pressure of the deposit around the well, since the flow rate Q of the well as measured in downhole conditions is then equal merely to:
Q=IP.xcex94
This downhole flow rate is then evacuated to the surface using means that are known in themselves.
In order to optimize production from a well, in particular an oil well, it is therefore useful to know its reserve quality, in particular by determining the values of certain defined parameters. Referring to the expression for the productivity index IP given above, a first important parameter is the permeability k of the productive layer of the subsoil in which the well has been drilled, and another is the xe2x80x9cskinxe2x80x9d S which quantifies possible damage to the productive layer. It is thus possible to establish two classes of well from which production is low: wells that are maintained under ideal operating conditions (S=0) but which are taking oil from rock that has low permeability; and wells drilled in deposits presenting high permeability, but which have become clogged (S greater than 0) and which could produce more after being restored by using techniques that are themselves known.
It is therefore important to be able to detect the formation of a layer of clogging in order to take action as soon as possible in effective manner to eliminate that layer and to continue working the well.
Various methods have been developed for monitoring the production quality of a well. Most of the old methods are based on using empirical or statistical relationships between various measurements that can be performed on such a well. Another method giving results that are more accurate consists in completely closing the outlet of the well and in studying the rise in the pressure of the oil in the well as a function of closure time, where examination of curves plotting variation in said pressure makes it possible to deduce whether the well is in its ideal state or whether it is clogged.
That method makes it possible to obtain good results, but it presents the major drawback of being lengthy to implement. In order to obtain a curve that is useful, it is necessary to wait for several hours, or even several days with some wells, during which time the well is not in use, thus constituting certain loss of production, to which there needs to be added the cost of restarting when the pressure of the deposit is no longer sufficient for the well to remain eruptive.
To mitigate that drawback, attempts have been made to develop another method which consists in modulating closure of the well at its outlet and in studying the variation in the pressure of the fluid as a function of such modulation. That method eliminates the above-mentioned drawback of total closure of the well, but presents the drawback of leading to measurements that are not sufficiently accurate.
For example, another method is described in U.S. Pat. No. 3,559,476 and FR-A-2 678 679. It consists in modulating the flow rate of the fluid in the well by means of a sinewave function and in measuring the variations in the flow rate and the pressure of the fluid, from which the response R of the well is deduced in certain special cases.
That method gives results that are relatively satisfactory when the damage to the well consists in its wall being clogged so as to give a positive xe2x80x9cskinxe2x80x9d value, and providing the xe2x80x9cskinxe2x80x9d has thickness that can be assumed to be zero. Clearly that type of infinitely thin xe2x80x9cskinxe2x80x9d is merely a convenient mathematical abstraction which is often satisfactory, but other types of damage can exist which correspond to a positive value for the xe2x80x9cskinxe2x80x9d but for which the thickness of the xe2x80x9cskinxe2x80x9d cannot be taken as being zero, or which correspond to a negative value for the xe2x80x9cskinxe2x80x9d, for example when a well is connected to a network of natural cracks that are open or when a well is being stimulated by hydraulic fracturing, i.e. has an artificially induced fracture passing through it, which fracture is generally symmetrical relative to the axis of the well.
An object of the present invention is thus to mitigate the above-mentioned drawbacks of prior methods of evaluating the reserve quality of an oil well or the like, and to provide a method which, while being easy to implement, nevertheless enables such evaluation to be performed at all levels of the well and regardless of the type of damage to the productive layer, by means of measurements which can be interpreted with a low error percentage of uncertainty.
Another object of the present invention is to provide apparatus enabling the method to be implemented.
More precisely, the present invention provides a method of determining the reserve quality of an oil well or the like delivering a given fluid coming from a productive layer, by measuring the response R of the well, said method consisting in modulating the flow rate of the fluid in the well by means of a sinewave function, and in measuring the variations in the flow rate and the pressures of the fluid, the method being characterized by the fact that:
I) the response Rc of the well when said productive layer includes a damaged zone presenting a positive xe2x80x9cskinxe2x80x9d value S for xe2x80x9cskinxe2x80x9d of non-zero thickness is obtained by the equation:             R      c        =                                        D                          R              0                                ⁡                      (                          β              ⁢                              xe2x80x83                            ⁢                              z                w                                      )                          -        B                              -                                    C                              R                0                                      ⁡                          (                              β                ⁢                                  xe2x80x83                                ⁢                                  z                  w                                            )                                      +        A              ,
xe2x80x83and that
II) the response Rf of the well when the productive layer has a fracture presenting a negative xe2x80x9cskinxe2x80x9d value S is obtained by the equation:       R    f    =            π                        F          CD                ⁢                                                            i                                  Z                  f                                2                                            E                fD                                      +                                          2                ⁢                                                      i                                                        Z                    f                                                                              F                CD                                                          +          S      wf      
xe2x80x83in which equations:
A, B, C, and D are functions of the parameters zw, xcex1, and xcex2, as defined below, and are respectively defined by the following four equations:                                                                         A                ⁢                                  (                                      z                    w                                                  ⁢                                  ,                  α                  ,                  β                                )                            =                            ⁢                              i                ⁢                                  xe2x80x83                                ⁢                                                      z                    w                                                        α                                                  ⁢                                                      ⅇ                                                                  ⅈ                        ⁢                                                  xe2x80x83                                                ⁢                        π                                            4                                                        [                                                                                                              kelbe                          0                                                ⁡                                                  (                                                                                    β                                                              z                                w                                                                                                                    α                                                                                )                                                                    ⁢                                                                        kelke                          1                                                ⁡                                                  (                                                                                    z                              w                                                                                      α                                                                                )                                                                                      -                                                                                                                                        ⁢                                                                    kelbe                    1                                    ⁡                                      (                                                                  z                        w                                                                    α                                                              )                                                  ⁢                                                      kelke                    0                                    ⁡                                      (                                                                  β                                                  z                          w                                                                                            α                                                              )                                                              ]                                                                                                                  B                ⁢                                  (                                      z                    w                                                  ⁢                                  ,                  α                  ,                  β                                )                            =                            ⁢                                                1                  α                                [                                                                                                    kelbe                        0                                            ⁡                                              (                                                                              z                            w                                                                                α                                                                          )                                                              ⁢                                                                  kelke                        0                                            ⁡                                              (                                                                              β                            ⁢                                                          xe2x80x83                                                        ⁢                                                          z                              w                                                                                                            α                                                                          )                                                                              -                                                                                                                      ⁢                                                                    kelbe                    0                                    ⁡                                      (                                                                  β                                                  z                          w                                                                                            α                                                              )                                                  ⁢                                                      kelke                    0                                    ⁡                                      (                                                                  z                        w                                                                    α                                                              )                                                              ]                                                                                                                  C                ⁢                                  (                                      z                    w                                                  ⁢                                  ,                  α                  ,                  β                                )                            =                            ⁢                              i                ⁢                                  xe2x80x83                                ⁢                                                      β                                          z                      w                                        2                                    [                                                                                                              kelbe                          1                                                ⁡                                                  (                                                                                    z                              w                                                                                      α                                                                                )                                                                    ⁢                                                                        kelbe                          1                                                ⁡                                                  (                                                                                    β                              ⁢                                                              xe2x80x83                                                            ⁢                                                              z                                w                                                                                                                    α                                                                                )                                                                                      -                                                                                                                                        ⁢                                                                    kelbe                    1                                    ⁡                                      (                                                                  β                                                  z                          w                                                                                            α                                                              )                                                  ⁢                                                      kelke                    1                                    ⁡                                      (                                                                  z                        w                                                                    α                                                              )                                                              ]                                                                                                                  D                ⁢                                  (                                      z                    w                                                  ⁢                                  ,                  α                  ,                  β                                )                            =                            ⁢                              i                ⁢                                                      β                                          z                      w                                                                            α                                                  ⁢                                                      ⅇ                                                                  ⅈ                        ⁢                                                  xe2x80x83                                                ⁢                        π                                            4                                                        [                                                                                                              kelbe                          0                                                ⁡                                                  (                                                                                    z                              w                                                                                      α                                                                                )                                                                    ⁢                                                                        kelke                          1                                                ⁡                                                  (                                                                                    β                              ⁢                                                              xe2x80x83                                                            ⁢                                                              z                                w                                                                                                                    α                                                                                )                                                                                      -                                                                                                                                        ⁢                                                                    kelbe                    1                                    ⁡                                      (                                                                  β                                                  z                          w                                                                                            α                                                              )                                                  ⁢                                                      kelke                    0                                    ⁡                                      (                                                                  z                        w                                                                    α                                                              )                                                              ]                                          
xe2x80x83it being specified that in the equations given above:
kelken(x)=kern(x)+i kein(x)
xe2x80x83and
kelben(x)=bern(x)+i bein(x)
where i is the imaginary unit number in the mathematical theory of complex numbers and where kern, kein, bern, and bein are Kelvin functions;   α  =            k      s        k  
is the non-dimensional permeability of the damaged zone, ks representing the permeability of the damaged zone, and k representing the permeability of the productive layer;   β  =            r      s              r      w      
is the non-dimensional radius of the damaged zone, rs representing the radius of the damaged zone, and rw representing the radius of the well;       z    w    =            r      w        ⁢                  ω        δ            
where xcfx89 is the angular frequency of the sinewave function and xcex4 is the diffusivity of the productive layer equal to       k          ϕ      ⁢              xe2x80x83            ⁢      μ      ⁢              xe2x80x83            ⁢              c        t              ,
xcfx86 representing the porosity of the productive layer, xcexc representing the viscosity of the fluid, and ct representing the total compressibility of the fluid;       R    0    =                    K        0            ⁡              (                              i                                z            w                          )                                      i                                      z            w                    ⁢                      K            1                              ⁢              (                              i                                z            w                          )            
where K0 and K1 are modified Hankel functions; and also with       z    f    =            x      f        ⁢                  ω        δ            
where xf is the length of one of the wings of the fracture which is assumed to have two wings; FCD is the non-dimensional conductivity of the fracture represented by the formula                     k        f            ⁢      w              kx      f        ,
where kf represents the permeability of the material supporting the fracture and w represents the mean thickness of the supported fracture;       E    fD    =                    k        f            ⁢      ϕ      ⁢              xe2x80x83            ⁢              c        t                    k      ⁢              xe2x80x83            ⁢              ϕ        f            ⁢              c        tf            
is the non-dimensional diffusivity of the fracture, xcfx86f representing the porosity of the support material filling the fracture, and ctf representing the total compressibility of the fluid in the fracture; Swf is a xe2x80x9cskinxe2x80x9d if any, existing between the bottom of the well and the entry of the fracture.
The present invention also provides apparatus for implementing the above-defined method.